Formulation And Numerical Solution Of Quantum Control Problems

Formulation And Numerical Solution Of Quantum Control Problems Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Formulation And Numerical Solution Of Quantum Control Problems book. This book definitely worth reading, it is an incredibly well-written.

Formulation and Numerical Solution of Quantum Control Problems

Alfio Borzi,Gabriele Ciaramella,Martin Sprengel
Formulation and Numerical Solution of Quantum Control Problems Book PDF

Author : Alfio Borzi,Gabriele Ciaramella,Martin Sprengel
Publisher : SIAM
Page : 396 pages
File Size : 45,9 Mb
Release : 2017-07-06
Category : Technology & Engineering
ISBN : 9781611974836

Get Book

Formulation and Numerical Solution of Quantum Control Problems by Alfio Borzi,Gabriele Ciaramella,Martin Sprengel Pdf

This book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the Schr?dinger picture, and the optimization theory, which focuses on functional spaces, is based on the Lagrange formalism. The computational techniques represent recent developments that have resulted from combining modern numerical techniques for quantum evolutionary equations with sophisticated optimization schemes. Both finite and infinite-dimensional models are discussed, including the three-level Lambda system arising in quantum optics, multispin systems in NMR, a charged particle in a well potential, Bose?Einstein condensates, multiparticle spin systems, and multiparticle models in the time-dependent density functional framework. This self-contained book covers the formulation, analysis, and numerical solution of quantum control problems and bridges scientific computing, optimal control and exact controllability, optimization with differential models, and the sciences and engineering that require quantum control methods. ??

Formulation and Numerical Solution of Quantum Control Problems

Alfio Borzi,Gabriele Ciaramella,Martin Sprengel
Formulation and Numerical Solution of Quantum Control Problems Book PDF

Author : Alfio Borzi,Gabriele Ciaramella,Martin Sprengel
Publisher : SIAM
Page : 390 pages
File Size : 54,6 Mb
Release : 2017-07-06
Category : Technology & Engineering
ISBN : 9781611974843

Get Book

Formulation and Numerical Solution of Quantum Control Problems by Alfio Borzi,Gabriele Ciaramella,Martin Sprengel Pdf

This book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the SchrÓdinger picture, and the optimization theory, which focuses on functional spaces, is based on the Lagrange formalism. The computational techniques represent recent developments that have resulted from combining modern numerical techniques for quantum evolutionary equations with sophisticated optimization schemes. Both finite and infinite-dimensional models are discussed, including the three-level Lambda system arising in quantum optics, multispin systems in NMR, a charged particle in a well potential, Bose?Einstein condensates, multiparticle spin systems, and multiparticle models in the time-dependent density functional framework. This self-contained book covers the formulation, analysis, and numerical solution of quantum control problems and bridges scientific computing, optimal control and exact controllability, optimization with differential models, and the sciences and engineering that require quantum control methods.

A First Course in Numerical Methods

Uri M. Ascher,Chen Greif
A First Course in Numerical Methods Book PDF

Author : Uri M. Ascher,Chen Greif
Publisher : SIAM
Page : 574 pages
File Size : 55,9 Mb
Release : 2011-07-14
Category : Mathematics
ISBN : 9780898719987

Get Book

A First Course in Numerical Methods by Uri M. Ascher,Chen Greif Pdf

Offers students a practical knowledge of modern techniques in scientific computing.

Numerical Methods for Conservation Laws

Jan S. Hesthaven
Numerical Methods for Conservation Laws Book PDF

Author : Jan S. Hesthaven
Publisher : SIAM
Page : 570 pages
File Size : 49,6 Mb
Release : 2018-01-30
Category : Science
ISBN : 9781611975109

Get Book

Numerical Methods for Conservation Laws by Jan S. Hesthaven Pdf

Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods; includes MATLAB software with which all main methods and computational results in the book can be reproduced; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material will be available online at publication.

Computational Uncertainty Quantification for Inverse Problems

Johnathan M. Bardsley
Computational Uncertainty Quantification for Inverse Problems Book PDF

Author : Johnathan M. Bardsley
Publisher : SIAM
Page : 141 pages
File Size : 50,5 Mb
Release : 2018-08-01
Category : Science
ISBN : 9781611975376

Get Book

Computational Uncertainty Quantification for Inverse Problems by Johnathan M. Bardsley Pdf

This book is an introduction to both computational inverse problems and uncertainty quantification (UQ) for inverse problems. The book also presents more advanced material on Bayesian methods and UQ, including Markov chain Monte Carlo sampling methods for UQ in inverse problems. Each chapter contains MATLAB? code that implements the algorithms and generates the figures, as well as a large number of exercises accessible to both graduate students and researchers. Computational Uncertainty Quantification for Inverse Problems is intended for graduate students, researchers, and applied scientists. It is appropriate for courses on computational inverse problems, Bayesian methods for inverse problems, and UQ methods for inverse problems.

The Sequential Quadratic Hamiltonian Method

Alfio Borzì
The Sequential Quadratic Hamiltonian Method Book PDF

Author : Alfio Borzì
Publisher : CRC Press
Page : 391 pages
File Size : 42,9 Mb
Release : 2023-05-26
Category : Mathematics
ISBN : 9781000882476

Get Book

The Sequential Quadratic Hamiltonian Method by Alfio Borzì Pdf

The sequential quadratic hamiltonian (SQH) method is a novel numerical optimization procedure for solving optimal control problems governed by differential models. It is based on the characterisation of optimal controls in the framework of the Pontryagin maximum principle (PMP). The SQH method is a powerful computational methodology that is capable of development in many directions. The Sequential Quadratic Hamiltonian Method: Solving Optimal Control Problems discusses its analysis and use in solving nonsmooth ODE control problems, relaxed ODE control problems, stochastic control problems, mixed-integer control problems, PDE control problems, inverse PDE problems, differential Nash game problems, and problems related to residual neural networks. This book may serve as a textbook for undergraduate and graduate students, and as an introduction for researchers in sciences and engineering who intend to further develop the SQH method or wish to use it as a numerical tool for solving challenging optimal control problems and for investigating the Pontryagin maximum principle on new optimisation problems. Features Provides insight into mathematical and computational issues concerning optimal control problems, while discussing many differential models of interest in different disciplines. Suitable for undergraduate and graduate students and as an introduction for researchers in sciences and engineering. Accompanied by codes which allow the reader to apply the SQH method to solve many different optimal control and optimisation problems.

Modelling with Ordinary Differential Equations

Alfio Borzì
Modelling with Ordinary Differential Equations Book PDF

Author : Alfio Borzì
Publisher : CRC Press
Page : 339 pages
File Size : 54,5 Mb
Release : 2020-04-13
Category : Mathematics
ISBN : 9781351190374

Get Book

Modelling with Ordinary Differential Equations by Alfio Borzì Pdf

Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games. The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book. Features: Provides insight into rigorous mathematical issues concerning various topics, while discussing many different models of interest in different disciplines (biology, chemistry, economics, medicine, physics, social sciences, etc.) Suitable for undergraduate and graduate students and as an introduction for researchers in engineering and the sciences Accompanied by codes which allow the reader to apply the numerical methods discussed in this book in those cases where analytical solutions are not available

Interpolatory Methods for Model Reduction

A. C. Antoulas,C. A. Beattie,S. Güğercin
Interpolatory Methods for Model Reduction Book PDF

Author : A. C. Antoulas,C. A. Beattie,S. Güğercin
Publisher : SIAM
Page : 244 pages
File Size : 41,8 Mb
Release : 2020-01-13
Category : Mathematics
ISBN : 9781611976083

Get Book

Interpolatory Methods for Model Reduction by A. C. Antoulas,C. A. Beattie,S. Güğercin Pdf

Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks. This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.

Methods in Computational Science

Johan Hoffman
Methods in Computational Science Book PDF

Author : Johan Hoffman
Publisher : SIAM
Page : 425 pages
File Size : 47,9 Mb
Release : 2021-10-19
Category : Computers
ISBN : 9781611976724

Get Book

Methods in Computational Science by Johan Hoffman Pdf

Computational methods are an integral part of most scientific disciplines, and a rudimentary understanding of their potential and limitations is essential for any scientist or engineer. This textbook introduces computational science through a set of methods and algorithms, with the aim of familiarizing the reader with the field’s theoretical foundations and providing the practical skills to use and develop computational methods. Centered around a set of fundamental algorithms presented in the form of pseudocode, this self-contained textbook extends the classical syllabus with new material, including high performance computing, adjoint methods, machine learning, randomized algorithms, and quantum computing. It presents theoretical material alongside several examples and exercises and provides Python implementations of many key algorithms. Methods in Computational Science is for advanced undergraduate and graduate-level students studying computer science and data science. It can also be used to support continuous learning for practicing mathematicians, data scientists, computer scientists, and engineers in the field of computational science. It is appropriate for courses in advanced numerical analysis, data science, numerical optimization, and approximation theory.

Advanced Reduced Order Methods and Applications in Computational Fluid Dynamics

Gianluigi Rozza,Giovananni Stabile,Francesco Ballarin
Advanced Reduced Order Methods and Applications in Computational Fluid Dynamics Book PDF

Author : Gianluigi Rozza,Giovananni Stabile,Francesco Ballarin
Publisher : SIAM
Page : 501 pages
File Size : 41,5 Mb
Release : 2022-11-21
Category : Mathematics
ISBN : 9781611977257

Get Book

Advanced Reduced Order Methods and Applications in Computational Fluid Dynamics by Gianluigi Rozza,Giovananni Stabile,Francesco Ballarin Pdf

Reduced order modeling is an important, growing field in computational science and engineering, and this is the first book to address the subject in relation to computational fluid dynamics. It focuses on complex parametrization of shapes for their optimization and includes recent developments in advanced topics such as turbulence, stability of flows, inverse problems, optimization, and flow control, as well as applications. This book will be of interest to researchers and graduate students in the field of reduced order modeling.

An Introduction to Compressed Sensing

M. Vidyasagar
An Introduction to Compressed Sensing Book PDF

Author : M. Vidyasagar
Publisher : SIAM
Page : 341 pages
File Size : 42,6 Mb
Release : 2019-12-03
Category : Technology & Engineering
ISBN : 9781611976120

Get Book

An Introduction to Compressed Sensing by M. Vidyasagar Pdf

Compressed sensing is a relatively recent area of research that refers to the recovery of high-dimensional but low-complexity objects from a limited number of measurements. The topic has applications to signal/image processing and computer algorithms, and it draws from a variety of mathematical techniques such as graph theory, probability theory, linear algebra, and optimization. The author presents significant concepts never before discussed as well as new advances in the theory, providing an in-depth initiation to the field of compressed sensing. An Introduction to Compressed Sensing contains substantial material on graph theory and the design of binary measurement matrices, which is missing in recent texts despite being poised to play a key role in the future of compressed sensing theory. It also covers several new developments in the field and is the only book to thoroughly study the problem of matrix recovery. The book supplies relevant results alongside their proofs in a compact and streamlined presentation that is easy to navigate. The core audience for this book is engineers, computer scientists, and statisticians who are interested in compressed sensing. Professionals working in image processing, speech processing, or seismic signal processing will also find the book of interest.

Vector Extrapolation Methods with Applications

Avram Sidi
Vector Extrapolation Methods with Applications Book PDF

Author : Avram Sidi
Publisher : SIAM
Page : 433 pages
File Size : 46,5 Mb
Release : 2017-09-26
Category : Science
ISBN : 9781611974966

Get Book

Vector Extrapolation Methods with Applications by Avram Sidi Pdf

An important problem that arises in different disciplines of science and engineering is that of computing limits of sequences of vectors of very large dimension. Such sequences arise, for example, in the numerical solution of systems of linear and nonlinear equations by fixed-point iterative methods, and their limits are simply the required solutions to these systems. The convergence of these sequences, which is very slow in many cases, can be accelerated successfully by using suitable vector extrapolation methods. Vector Extrapolation Methods with Applications is the first book fully dedicated to the subject of vector extrapolation methods. It is a self-contained, up-to-date, and state-of-the-art reference on the theory and practice of the most useful methods. It covers all aspects of the subject, including development of the methods, their convergence study, numerically stable algorithms for their implementation, and their various applications. It also provides complete proofs in most places. As an interesting application, the author shows how these methods give rise to rational approximation procedures for vector-valued functions in the complex plane, a subject of importance in model reduction problems among others. This book is intended for numerical analysts, applied mathematicians, and computational scientists and engineers in fields such as computational fluid dynamics, structures, and mechanical and electrical engineering, to name a few. Since it provides complete proofs in most places, it can also serve as a textbook in courses on acceleration of convergence of iterative vector processes, for example.

Sparse Polynomial Approximation of High-Dimensional Functions

Ben Adcock ,Simone Brugiapaglia,Clayton G. Webster
Sparse Polynomial Approximation of High Dimensional Functions Book PDF

Author : Ben Adcock ,Simone Brugiapaglia,Clayton G. Webster
Publisher : SIAM
Page : 310 pages
File Size : 53,6 Mb
Release : 2022-02-16
Category : Mathematics
ISBN : 9781611976885

Get Book

Sparse Polynomial Approximation of High-Dimensional Functions by Ben Adcock ,Simone Brugiapaglia,Clayton G. Webster Pdf

Over seventy years ago, Richard Bellman coined the term “the curse of dimensionality” to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book’s companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.

Mathematical Foundations of Finite Elements and Iterative Solvers

SCI085000
Mathematical Foundations of Finite Elements and Iterative Solvers Book PDF

Author : SCI085000
Publisher : SIAM
Page : 186 pages
File Size : 48,8 Mb
Release : 2022-06-27
Category : Mathematics
ISBN : 9781611977097

Get Book

Mathematical Foundations of Finite Elements and Iterative Solvers by SCI085000 Pdf

“This book combines an updated look, at an advanced level, of the mathematical theory of the finite element method (including some important recent developments), and a presentation of many of the standard iterative methods for the numerical solution of the linear system of equations that results from finite element discretization, including saddle point problems arising from mixed finite element approximation. For the reader with some prior background in the subject, this text clarifies the importance of the essential ideas and provides a deeper understanding of how the basic concepts fit together.” — Richard S. Falk, Rutgers University “Students of applied mathematics, engineering, and science will welcome this insightful and carefully crafted introduction to the mathematics of finite elements and to algorithms for iterative solvers. Concise, descriptive, and entertaining, the text covers all of the key mathematical ideas and concepts dealing with finite element approximations of problems in mechanics and physics governed by partial differential equations while interweaving basic concepts on Sobolev spaces and basic theorems of functional analysis presented in an effective tutorial style.” — J. Tinsley Oden, The University of Texas at Austin This textbook describes the mathematical principles of the finite element method, a technique that turns a (linear) partial differential equation into a discrete linear system, often amenable to fast linear algebra. Reflecting the author’s decade of experience in the field, Mathematical Foundations of Finite Elements and Iterative Solvers examines the crucial interplay between analysis, discretization, and computations in modern numerical analysis; furthermore, it recounts historical developments leading to current state-of-the-art techniques. While self-contained, this textbook provides a clear and in-depth discussion of several topics, including elliptic problems, continuous Galerkin methods, iterative solvers, advection-diffusion problems, and saddle point problems. Accessible to readers with a beginning background in functional analysis and linear algebra, this text can be used in graduate-level courses on advanced numerical analysis, data science, numerical optimization, and approximation theory. Professionals in numerical analysis and finite element methods will also find the book of interest.

Basics and Trends in Sensitivity Analysis: Theory and Practice in R

Sébastien Da Veiga,Fabrice Gamboa,Bertrand Iooss,Clémentine Prieur
Basics and Trends in Sensitivity Analysis Theory and Practice in R Book PDF

Author : Sébastien Da Veiga,Fabrice Gamboa,Bertrand Iooss,Clémentine Prieur
Publisher : SIAM
Page : 307 pages
File Size : 55,9 Mb
Release : 2021-10-14
Category : Mathematics
ISBN : 9781611976694

Get Book

Basics and Trends in Sensitivity Analysis: Theory and Practice in R by Sébastien Da Veiga,Fabrice Gamboa,Bertrand Iooss,Clémentine Prieur Pdf

This book provides an overview of global sensitivity analysis methods and algorithms, including their theoretical basis and mathematical properties. The authors use a practical point of view and real case studies as well as numerous examples, and applications of the different approaches are illustrated throughout using R code to explain their usage and usefulness in practice. Basics and Trends in Sensitivity Analysis: Theory and Practice in R covers a lot of material, including theoretical aspects of Sobol’ indices as well as sampling-based formulas, spectral methods, and metamodel-based approaches for estimation purposes; screening techniques devoted to identifying influential and noninfluential inputs; variance-based measures when model inputs are statistically dependent (and several other approaches that go beyond variance-based sensitivity measures); and a case study in R related to a COVID-19 epidemic model where the full workflow of sensitivity analysis combining several techniques is presented. This book is intended for engineers, researchers, and undergraduate students who use complex numerical models and have an interest in sensitivity analysis techniques and is appropriate for anyone with a solid mathematical background in basic statistical and probability theories who develops and uses numerical models in all scientific and engineering domains.